Multi-robot adversarial patrolling strategies via lattice paths

In full-knowledge multi-robot adversarial patrolling, a group of robots has to detect an adversary who knows the robots' strategy. The can easily take advantage any deterministic patrolling strategy, which necessitates employment randomised While Markov decision process been dominant methodology in computing penetration detection probabilities on polylines, we apply enumerative combinatorics characterise for four configurations. It allows us provide closed formulae these and facilitates characterising optimal random defence strategies. Comparing iteratively updating transition matrices, empirically show that our method reduces runtime by up several hours. This extensive simulations two robot movement types perimeter showing with direction is 0.4 more likely adversary. Therefore, approach greatly benefits theoretical empirical analysis strategies extendability complicated attacks other structured environments.